This paper presents a nonlinear model of human brain activity in response to visual stimuli according to Blood-Oxygen-Level-Dependent (BOLD) signals scanned by functional Magnetic Resonance Imaging (fMRI). A BOLD signal often contains a low frequency signal component (trend), which is usually removed by detrending because it is considered a part of noise. However, such detrending could destroy the dynamics of the BOLD signal and ignore an essential component in the response. This paper shows a model that, in the absence of detrending, can predict the BOLD signal with smaller errors than existing models. The presented model also has low Schwarz information criterion, which implies that it will be less likely to overfit the experimental data. Comparison between the various types of artificial trends suggests that the trends are not merely the result of noise in the BOLD signal.

Phase structure of nonlinear dynamical system is governed by the vector field and decides the trajectories. Accordingly, the power spectra of trajectories include the structural field effect on the phase space. In this paper, we develop a method for analyzing phase structure using power spectra of trajectories and reconstitute a potential function in the system.

Quad-core cpus have been a common desktop configuration for today's office. The increasing number of processors on a single chip opens new opportunity for parallel computing. Our goal is to make use of the multi-core as well as multi-processor architectures to speed up large-scale data mining algorithms. In this paper, we present a general parallel learning framework, Cut-And-Stitch, for training hidden Markov chain models. Particularly, we propose two model-specific variants, CAS-LDS for learning linear dynamical systems (LDS) and CAS-HMM for learning hidden Markov models (HMM). Our main contribution is a novel method to handle the data dependencies due to the chain structure of hidden variables, so as to parallelize the EM-based parameter learning algorithm. We implement CAS-LDS and CAS-HMM using OpenMP on two supercomputers and a quad-core commercial desktop. The experimental results show that parallel algorithms using Cut-And-Stitch achieve comparable accuracy and almost linear speedups over the traditional serial version.

In this paper, we propose a variational method to derive the coefficients of piecewise-linear (PWL) models able to accurately approximate nonlinear functions, which are vector fields of autonomous dynamical systems described by continuous-time state-space models dependent on parameters. Such dynamical systems admit limit cycles, and the supercritical Hopf bifurcation normal form is chosen as an example of a system to be approximated. The robustness of the approximations is checked, with a view to circuit implementations.

Acoustic modeling in speech recognition uses very little knowledge of the speech production process. At many levels our models continue to model speech as a surface phenomenon. Typically, hidden Markov model (HMM) parameters operate primarily in the acoustic space or in a linear transformation thereof; state-to-state evolution is modeled only crudely, with no explicit relationship between states, such as would be afforded by the use of phonetic features commonly used by linguists to describe speech phenomena, or by the continuity and smoothness of the production parameters governing speech. This survey article attempts to provide an overview of proposals by several researchers for improving acoustic modeling in these regards. Such topics as the controversial Motor Theory of Speech Perception, work by Hogden explicitly using a continuity constraint in a pseudo-articulatory domain, the Kalman filter based Hidden Dynamic Model, and work by many groups showing the benefits of using articulatory features instead of phones as the underlying units of speech, will be covered.

In this paper, an iterative decoding algorithm for channels with additive linear dynamical noise is presented. The proposed algorithm is based on the tightly coupled two inference algorithms: the sum-product algorithm which infers the information symbols of an low density parity check (LDPC) code and the Kalman smoothing algorithm which infers the channel states. The linear dynamical noise are the noise generated from a linear dynamical system. We often encounter such noise (i.e., additive colored noise) in practical communication and storage systems. The conventional iterative decoding algorithms such as the sum-product algorithm cannot derive full potential of turbo codes nor LDPC codes over such a channel because the conventional algorithms are designed under the independence assumption on the noise. Several simulations have been performed to assess the performance of the proposed algorithm. From the simulation results, it can be concluded that the Kalman smoothing algorithm deserves to be implemented in a decoder when the linear dynamical part of the linear dynamical noise is dominant rather than the white Gaussian noise part. In such a case, the performance of the proposed algorithm is far superior to that of the conventional algorithm.

A merged analog-digital circuit architecture is proposed for implementing intelligence in SoC systems. Pulse modulation signals are introduced for time-domain massively parallel analog signal processing, and also for interfacing analog and digital worlds naturally within the SoC VLSI chip. Principles and applications of pulse-domain linear arithmetic processing are explored, and the results are expanded to the nonlinear signal processing, including an arbitrary chaos generation and continuous-time dynamical systems with nonlinear oscillation. Silicon implementations of the circuits employing the proposed architecture are fully described.

We investigate bifurcations of the periodic solution observed in a phase converter circuit. The system equations can be considered as a nonlinear coupled system with Duffing's equation and an equation describing a parametric excitation circuit. In this system there are two types of solutions. One is with x = y = 0 which is the same as the solution of Duffing's equation (correspond to uncoupled case), another solution is with xy0. We obtain bifurcation sets of both solutions and discuss how does the coupling change the bifurcation structure. From numerical analysis we obtain a codimension two bifurcation which is intersection of double period-doubling bifurcations. Pericdic solutions generated by these bifurcations become chaotic states through a cascade of codimension three bifurcations which are intersections of D-type of branchings and period-doubling bifurcations.

We propose an equivalent circuit model described by the Rössler equation. Then we can consider a coupled Rössler system with a physical meaning on the connection. We consider an oscillatory circuit such that two identical Rössler circuits are coupled by a resistor. We have studied three routes to entirely and almost synchronized chaotic attractors from phase-locked periodic oscillations. Moreover, to simplify understanding of synchronization phenomena in the coupled Rössler system, we investigate a mutually coupled map that shows analogous locking properties to the coupled Rössler System.